Question

For a first order reaction, $A \longrightarrow B$, the reaction rate at reactant concentration of $0.01\, M$ is found to be $2.0 \times 10^{-5} \, mol \, \, L^{-1} s^{-1}$. The half-life period of the reaction is

• A. 220 s
• B. 30 s
• C. 300 s
• D. 347 s

Answer 1

Answer: (D)

For first order reaction,
$ A \longrightarrow B$
$$ rate = k x [A]
$ Rate =2.0 \times 10^{-5} mol \, \, L^{-1} s^{-1}$
$ [A]=$0.01 M
So, $2.0 \times 10^{-5}=k \times 0.01$
$ k=\frac{2.0 \times 10^{-5}}{0.01} s^{-1}$
$ =2.0 \times 10^{-3} s^{-1}$
For first order reaction,
$ t_{1/2}=\frac{0.693}{k}$
$ =\frac{0.693}{2.0 \times 10^{-3}}$
$ =346.5 \approx 347$ s